Benchmark for the Coupled Magneto-Mechanical Boundary Value Problem in Magneto-Active Elastomers.

Area of Science:

• Mechanics of Materials
• Computational Solid Mechanics
• Electromagnetism

Background:

• Magneto-active elastomers (MAEs) exhibit complex magneto-mechanical coupling.
• Experimental analysis is crucial for understanding MAE behavior.
• Validating computational models requires standardized benchmark problems.

Purpose of the Study:

• To present a novel benchmark problem for the coupled magneto-mechanical boundary value problem in MAEs.
• To enable validation of different computational modeling strategies.
• To provide a basis for future comparisons with advanced models and methods.

Main Methods:

• Development of a benchmark problem derived from experimental data.
• Comparison of a sharp-interface Lagrangian finite element framework with a diffuse-interface Eulerian approach.
• Analysis of simplified 2D and general 3D cases.

Main Results:

• Both modeling strategies show good agreement for the considered MAE material models.
• Discrepancies between methods are attributable to known literature effects.
• The influence of boundary conditions and sample size were analyzed.

Conclusions:

• The proposed benchmark problem effectively validates computational strategies for MAEs.
• The study confirms the reliability of both Lagrangian and Eulerian approaches for MAE simulations.
• This benchmark serves as a foundation for further research in MAE modeling.